Scaling laws describe memories of host–pathogen riposte in the HIV population

Significance A cure or a vaccine for HIV remains elusive, and HIV is not known to be cleared by natural immune responses. Thus, one can study how a virus evolves in humans in the absence of effective directed selection pressures and harness this knowledge to inform vaccine design. We find that the sequence space accessed by circulating HIV strains is characterized by sets of sequences related by collectively coupled mutations that evade host immunity (an informative lower-dimensional representation of sequence space). These sets of sequences represent stored memories of host–pathogen combat won by the virus (analogous to neural networks) and obey power law scaling. The collective escape pathways we reveal must be thwarted by an effective vaccine. The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host–pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.